Question

How do you simplify `(\frac { 4} { 9} - \frac { 1} { 3} ) \div \frac { 7} { 10}`?

Answer 1

See a solution process below:

Explanation:

First, execute the operation in parenthesis by putting the fractions over common denominators:

`(4/9 - [3/3 xx 1/3]) -: 7/10 =>`

`(4/9 - 3/9) -: 7/10 =>`

`((4 - 3)/9) -: 7/10 =>`

`1/9 -: 7/10`

Next, we can rewrite the expression as:

`(1/9)/(7/10)`

Now, we can use this rule for dividing fractions to complete the simplification:

`(color(red)(a)/color(blue)(b))/(color(green)(c)/color(purple)(d)) = (color(red)(a) xx color(purple)(d))/(color(blue)(b) xx color(green)(c))`

`(color(red)(1)/color(blue)(9))/(color(green)(7)/color(purple)(10)) => (color(red)(1) xx color(purple)(10))/(color(blue)(9) xx color(green)(7)) => 10/63`